1. Field of the Invention
The present invention relates to a laser scanner, and particularly it relates to a laser scanner and a non-spherical scanning lens suitable for use in high precision laser printers.
2. Description of the Prior Art
In a conventional laser printer, a laser beam 100 (FIG. 2) performs deflection scanning with the use of a rotary polyhedral mirror 10, to write information onto a scanning plane (photosensitive drum) 16. An F.theta. lens system is used to correct problems such as focusing (i.e. field curvature), disposition (i.e. aberration of distortion) and the like, which are produced on the scanning plane 16 during scanning. The field curvature refers to the defocusing characteristic of an image on the scanning plane. The F.theta. lens system 1 corrects the aberration of distortion and the field curvature so that the scanning angle and scanning position of the rotary polyhedral mirror 10 are proportional to each other. The conventional F.theta. lens system 1 includes two single lenses (first and second lenses 51 and 52).
However, one source of errors in the above-mentioned conventional scanning system is a side fall error of a rotary polyhedral mirror produced by processing which occurs during manufacturing. Therefore, an anamorphic optical system has been constructed with an F.theta. lens system which is made to include cylindrical surfaces or toric surfaces that provide a side fall correction function to correct the above-mentioned error. Examples of side fall corrective systems are disclosed in Japanese Patent Unexamined Publication Nos. Sho. 54-126051 and Sho. 57-144515 (Japanese Patent Examined Publication No. Hei. 1-15046) and Japanese Patent Examined Publication No. Hei. 1-14564.
The cylindrical surfaces or toric surfaces are generally applied to the second lens 52 which is the lens furthest from the rotary polyhedral mirror 10. It is preferable to place the cylindrical or toric surfaces on the second lens since, if the cylindrical or toric surfaces were applied to the first lens 51 (i.e. the lens nearest the rotary polyhedral mirror 10), then the lateral magnification in the sub-scanning direction would become too large (i.e., 5 or more). This enlarged lateral magnification would necessitate an extremely accurate arrangement between the rotary polyhedral mirror 10 and the F.theta. lens system 1.
Further, Japanese Patent Unexamined Publication No. Sho. 62-265615 discloses a technique for asymmetrically changing the curvature of the F.theta. lens system 1 in the direction vertical to the sub-scanning direction of the F.theta. lens system 1. This asymmetrical change occurs with respect to the rotary axis and is in accordance with the position of deflection, thereby correcting the above noted error.
In order to increase the precision, with which a laser printer draws figures, it is necessary to ensure that the field curvature falls within the depth of focus along the entire scanning plane. By maintaining the field curvature within the depth of focus, the system prevents defocusing of a very small laser spot and improves displacement, linearity, etc. in scanning, thereby improving the performance of the F.theta. lens system.
A conventional F.theta. lens system constructed with two single lenses, can correct sufficiently aberrations of distortion of third-order or less. However, it remains difficult to correct aberrations of distortion of fifth-order or more. More specifically, when laser beam scanning is performed with a wide viewing angle, there is a large influence due to distortion in the peripheral portion of the viewing angle. For example, an F.theta. characteristic value (i.e. the displacement characteristic on a scanning plane) is about 0.22% when the scanning width is 300 mm and the viewing angle is .+-.31.degree.. In this situation, the F.theta. characteristic value represents an error distance between a light spot (at which the beam focuses) and a scanning spot (at which the laser beam should focus) on a scanning plane. The F.theta. characteristic relates to the linearity of the relation between the laser beam's drawing point and the scanning angle of the rotary polyhedral mirror.
If the number of the lenses is increased to three or more, the F.theta. characteristic can be improved. However, this increases the number of parts and increases the complexity of assembly and thus, such a system could not be employed simply.
The correction limitation in the above-mentioned conventional F.theta. lens system will be described in more detail with reference to FIGS. 3-7.
FIG. 3 represents a top view of FIG. 2, and illustrates two parallel light beams 101 and 102, which have different entrance pupil positions. These parallel light beams are focused in the vicinity of an image-side focal plane 23 of the second lens 52. The points at which the light beams 101 and 102 intersect an optical axis 24 represent their entrance pupil positions 21 and 22 for the second lens 52. The entrance pupil positions affect the aberrations of distortion.
The first lens 51 includes concave lens surfaces 11 and 13 having axes of rotational symmetry. The second lens 52 includes a spherical or planar lens surface 14 having an axis of rotational symmetry, and a convex lens surface 15 which is rotationally asymmetric. The first lens 51 has a negative power (i.e. a beam incident thereto is bent away from the optical axis 24), and the second lens 52 has a positive power (i.e. a beam incident thereto is bent towards the optical axis 24). This positive and negative power arrangement tends to cause the scanning positions to shift toward the optical axis (negative side) along the outer peripheral portion of the scanning plane 16 for the entire F.theta. characteristic. This tendency can be corrected by moving the above-mentioned entrance pupil positions toward the second lens 52 as the scanning angles are increased.
FIG. 4 illustrates the relation between the ratio (as plotted along the ordinate) of the entrance pupil positions at the scanning angles 0.degree. and 31.degree., and the thickness t (as plotted along the abscissa) of the center portion of the first lens 51. The entrance pupil positions represents the distances measured from the lens surface 14 of the second lens 52 to the points at which a light beam intersects the optical axis 24. The relation in FIG. 4 was calculated while the shapes of the lens surfaces 11 and 13 remained constant. The ratio of the entrance pupil positions represent the ratio between the distance when the rotary mirror is at a scanning angle of 0.degree. and the distance when the rotary mirror is at a scanning angle of 31.degree.. FIG. 4 illustrates that it is desirable to increase the thickness t of the center portion of the first lens 51, because a more preferred result can be obtained if the entrance pupil positions are made closer to lens 51 when the scanning angle is large.
FIG. 5 illustrates the relation between the F.theta. characteristic and the scanning angle from 0.degree. to 31.degree., for three different thicknesses t of the center portion of the first lens 51. FIG. 5 shows that the F.theta. characteristic curve between the scanning angles of 0.degree. and 31.degree. is shifted towards the negative side as the thickness t of the first lens center portion is made thinner. Thus the above-mentioned entire F.theta. characteristic can be corrected if the thickness t of the center portion is increased. More directly, if changing the thickness t of the center portion of the first lens 51 only affected the F.theta. characteristic and the F.theta. characteristic was preferably below 0.15%, then the thickness t could be set to t .gtoreq.7.0 mm. However, changing the thickness t also changes other lens characteristics, as explained hereafter.
FIG. 6 shows the relationship between the field curvature and the scanning angle for three different thicknesses t of the center portion of the first lens 51, as the scanning angle varies from 0.degree. to 31.degree.. The field curvature represents the distance between the scanning plane 16 and the image point position along the image side focal plane 23. FIG. 6 illustrates that the image plane 23 tends to bend inward from the scanning plane 16 (i.e. toward the lens 52) when the thickness t of the center portion is 4.4 mm. The image plane tends to bend outward (i.e. away from the lens 52) when the thickness t is 7.0 mm. Thus, FIG. 6 illustrates that an optimum region for the thickness t exists which minimizes the field curvature and which positions the image plane on or substantially near the scanning plane 16.
Preferably, the field curvature is made within the depth of focus, which is, for example, about .+-.1.0 mm when the dot density is 480 dpi (dots per inch). The depth focus is approximately .+-.0.6 mm, when the dot density is 600 dpi. Both exemplary depths of focus assume that the laser's beam spot diameter is allowed to change up to 5% when the laser light has a wave length of 80 nm.
FIG. 7 illustrates the relation between the beam spreading angle ratio at scanning angles of 0.degree. and 31.degree. and the thickness t of the first lens 51. If the spreading angle of a beam incident on the second lens 52 can be made small at a position in which the scanning angle is large, then the field curvature can be reduced, even when the thickness t of the center portion is large. However, as shown in FIG. 7, the ratio of the above-mentioned spreading angles of an incident beam (i.e. the ratio between the spreading angle at a 0.degree. scanning angle and the spreading angle at a 31.degree. scanning angle) is substantially independent of the thickness t of the center portion of the first lens 51. Thus, it is difficult to reduce the spreading angle for improving the field curvature by changing the first lens' thickness t.
The results of the above analysis can be summarized as follows. The thickness t of the center portion of the first lens 51 can be used, as a practical design parameter, to improve the aberration of distortion or the field curvature in a conventional F.theta. lens system that includes two single lenses. However, the field curvature and F.theta. characteristic can not be improved simultaneously by adjusting the thickness of lens 51. Specifically, the field curvature cannot be corrected within the range of lens thicknesses t which provide a superior F.theta. characteristic.